Consumption data exploration

There is a good deal of heterogenity between different units

Timecourses appear to depend on the type of unit

Business consumption shows a strong weekly periodicity. The daily variation also looks different.

Product 2 shows small and often intermittant consumption.

Distribution of consumption values

The consumption is sharply peaked near zero. This may be due to the prevalence of small consumers

What does the daily variation around the mean look like?

From the plots, it looks the hour-to-hour variation is not the same between days: does it differ from normal?

It's not perfectly normal and the appears to be some multimodality, probably because it doesn't account for time factors. Nonetheless, this residual is reasonable for linear regression analysis

Linear regression analysis for one unit

For these fits, we need to account for interaction between time and season in particular to get good fits. Of course, adding weekday x season interactions improves the fits as well.

Coarser yearly features

This is not bad actually. There are still periods of large errors, and strong autocorrelation in the residuals, but it still looks like the fits are capturing the dominant periodic modes.

Some things that need validation:

1. The number of Fourier modes to use. (for some reason, more than 2 behaves very strangely)
2. The interaction basis between daily, weekly, and yearly factors
   • at the moment, I favor full interaction because it leads to autocorrelations that peak near 24 and 48 hours, which we know to probably be the case.

Introducting autocorrelation

Autocorrelations do indeed seem helpful.

I think that this is a good set of features to get started with.